how do we define a wave function?

[andrewhei]

what is a wave function? And how do we define a wave function? How is it related to schrodinger's equation?

[jtbell]

Are you asking about waves in general: water waves, light waves, sound waves, etc.? Or are you specifically asking about quantum mechanics?

And what's the background of your question? What level of physics are you studying now, how much math do you know, how far along are you in school, etc.? It's hard to answer questions when we have no idea what kind of answer is appropriate for you.

[andrewhei]

i am a hong kong form 7 student, 1 year from college.
i want to know about the wave funtion phi, in quantum mechanics, i only know that phi square is the probabilty density, but i don't quite understand what a wave function really is.
Also, i don't understand the derivation of the schrodiger equation.

[Fredrik]

It doesn't represent something measurable. It's a mathematical representation of the state of the system, and the Schrödinger equation describes how it changes with time. See #8 in this (http://www.physicsforums.com/showthread.php?t=237440) thread for a few more details. You should consider the Schrödinger equation a postulate, not a derived result. If you want to "derive" it, you're going to have to postulate something else first, e.g. what the solutions are.

[Diego Floor]

Just to complement.. The wave function can be mathematically defined simply as the solutions of the Schrödinger's equation, wich itself can't be derived. You can say the Schrödinger equation was constructed, so it describes the quantum mechanics as we observe it.

I don't think the wave functions have a direct physical interpretation. ( you have to obtain some real value from it, like it's square)